Radomes are usually made of lossy dielectric materials, and their accurate analysis is often cumbersome because of their typical large electrical size and geometrical complexity. In real reflector antenna structures, there are always complex interactions between the radome, the reflector surfaces and the directional feeds, which are typically neglected for the sake of simplicity. In this paper we will consider all such interactions in a very accurate way, thus requiring a high number of unknowns for the numerical solution of the problem. To overcome such drawback, an integral equation formulation based on the Equivalence Principle in combination with the wavelet transform has been employed, obtaining finally a robust and accurate CAD tool for the rigorous analysis of arbitrarily shaped radomes containing continuous and discrete electromagnetic sources. It will be shown that the use of wavelet-like bases substantially improves the numerical efficiency and memory requirements of the original integral equation method. For verification purposes, the results obtained with the new technique are successfully compared with examples taken from the literature. Complex antenna structures are then discussed in order to prove the usefulness of the new method.